Friday, January 20, 2012

Just before I hopped in the shower today, I picked up Carse's Finite and Infinite Games and reread a couple passages. In my esteem, James Carse deserves cannonization (sic.) as a 2nd-Class Saint of Eris, given that said book boils down to a case for the idea that all seriousness is contained within playfulness, rather than the other way around, and given the way his delightful Religious Case Against Belief points out that the complete acceptance of any literal religion as a guide appears to be an abdication of moral decision making in favor of letting some text decide for you.

Delightful as I find the books themselves, I'd rather talk about the train of thought the former set off in me. Reading the book I remembered the period soon after I'd first read it before finishing undergrad classes, and some of the discussions I had with fellow philosophy students. Of course, contention comes to memory more easily than quiescence, so my mind quickly drew back to a peer's point about the great difficulty in defining 'game' as Carse uses it in the book. Perhaps due to our shortsightedness, due to the lack of a cogent phrase, or simply due to misconceptions about what kind of definition would satisfy, we had no success, with effort, at defining the term in a way that seemed satisfactory. All the definitions proposed seemed either too limited in scope to fit the way the term comes up in the book, or so broad that we could see nearly anything in terms of games.

It was today that it dawned on me that that the latter doesn't actually a pose problem. If a term's definition has enough flexibility that the term can be applied to virtually anything, the term doesn't refer to an element of the world, it refers to way of framing our observations of the world.

Previously I've heard it argued that terms that can apply to anything, in fact, apply to nothing. This point holds water in that, if you treat everything as though it had a particular property, explanations in terms of that property tell you almost nothing. For instance, if we posited that the universe and all constituents thereof are 'wiggly', we could attempt to explain both the counter-intuitive results of the double-slit experiment and the poor record of intelligence tests at predicting future performance in terms of wiggles, but to the extent that we posited wiggles as explaining every nook and cranny we could project them into, we would simply create a semantic spook, like the imps medieval doctors posited to reside in the abdomen that caused stomach cramps. Similarly, atheists (and others) will readily note that explaining the unknown in terms of "God did it" and leaving it at that serves more as a veil than an explanation.

To this I offer the rejoinder that such explanations attempt to explain happenings in the universe in terms of some particular element of the universe (or, to preempt the quibbles of certain theologies, in terms of some element that has causal efficacy over the universe). We posit wiggles, God, or phlogiston as referent terms rather than as frames of reference. Games, however, as presented in the book, feel more like a way of looking at things than a set of elements that explain the operation of other elements. (It's worth noting that Carse does not make this distinction explicitly, but we challenge you to tell us how an infinite game would operate without multiple cognitive frames of reference.)

Now let's spend some time looking at the inherent barrier that sometimes hides the distinction between frames and elements from us. The primary one, as I see it, lies in the dominance of convergent thinking. If the distinction between convergent and divergent thinking doesn't ring a bell, convergent thinking involves the attempt to find one solution to fit all the evidence and moves onto a different once such a solution has been found; while divergent thinking entails finding many possible solutions to explain extant evidence, with more of a focus on creating possible answers than on eliminating possible answers to find the solution.

With convergent thinking, novel observations lead us to either find a more accurate way to describe the behavior of currently accepted elements of the world or to posit new elements such that their interaction with previously known elements explains the new phenomenon. Convergent thinking aims to create a mono-mega-model (MMM) for explaining everything smaller than the universe and larger than the Planck scale, so developing new models without a way to tie their framework into that of the MMM fragments our ability to understand the universe. The urge to convergent thinking gives the appearance of a crisis in modern physics, with the macrocosm explained in terms of the bending of continuous spacetime and the microcosm in terms of discrete quantized units of the same. We create new frameworks, but only with the intent of unifying what we previously dealt with in multiple different frames.

As David Bohm points out in Wholeness and the Implicate Order, chapter 5, each major tangible advance of science, each paradigm shift, indicates itself by the explanation of what were previously dealt with under different frameworks in terms of a unified order. Bohm, though hardly the exemplar of convergent thinking's worst shortcomings, still indicates some of them in his thought. He makes a strong stand in the first chapter against the widespread assumption our theories give us a complete and perfect picture of reality, checking the tendency of convergent thinking to lead to an MMM we believe in because we have nothing else, but he makes a very determined case against fragmentation. Though not opposed to divergent thinking, it seems pretty clear that he feels convergent thinking should act as the final arbiter of our ontology.

On the other hand, modern divergent thinking typically involves at least the tacit acceptance of confirmation bias as remarkably difficult to eliminate from thought - so difficult to eliminate, in fact, that you easily to think you've eliminated it when, in fact, you haven't. With divergent thinking one prefers to have multiple frames that explain the same phenomena than to narrow down to one on a permanent basis. This doesn't necessitate that the divergent thinker freezes when it comes to choosing a course of action where different frames point in different directions (though premature uncertainty poses as much a pitfall for divergent thinking as premature certainty does for convergent) - it simply involves coming up with multiple solutions to the same problem before riding off into the sunset on the back of the first seemingly cogent explanation.

Studies have shown that the brainwaves of creative women performing divergent thinking tasks tend to be asynchronous, while while those of creative men doing the same are more often coherent across the cerebral hemispheres. Given [pdf warning] that a significant portion more left-handed people (more often those who write with their hand above the text than those who write with their hand below it as most right-handed people do) have language centers outside the left hemisphere than do right-handed people, this indicates why left-handed men do markedly better on average than right-handed men do at divergent thinking tasks, while handedness does not appear to affect the performance of divergent thinking tasks for women. It also indicates an explanation for the cultural dominance of convergent thinking.

While the influence of women among intellectuals has markedly increased over the past several centuries, and left-handed males have an influence on politics and the like disproportionate to the amount of the population they constitute, by millennia of patriarchy and by sheer numbers, right-handed males, least likely to be particularly gifted at divergent thinking, have constituted the majority of influential positions in modern history. Hardly a surprise, then, that we often tacitly accept convergent thinking as the final arbiter of thought.

Now that we've examined the reason we tend to use ubiquitous terms (terms that can be applied to nearly everything, remember) as elements rather than frames, let's time to look at the two with an eye toward recursion. Of course, in the frame we've looked into here, we see frame and element as the two major elements. Distinguishing between referents and frames of reference comes in handy when looking at perspectives, but it is still but a way of looking. Seen through its own eye, it assumes that all ways of looking have assumptions underlying them so that it can compare those, and places perspectives in terms of the frame that created them rather than their content.

This arrangement reminds me of the epistemic paradox underlying much of post-modernism: why trust the frame that tells us no frame is privileged over various frames which claim that they are privileged? As tempting as we find it to say that any frame which makes an idol of itself sells itself short when it comes to seeing the whole truth, enacting this belief idolizes frames that don't affirm their own truth via circular logic. Such seeking to winnow away frames seems to bear the mark of our favoring of convergent thinking over divergent. If we don't expect to find singular truth for the sake of accommodating our habits of thought, little issue arises with holding many frames in approximately equal esteem.

In the opposite direction, taking frames as elements, we find a frame that shows us various ways of interpreting perception as elements acting upon the sphere of human action. Such a frame would resemble the one used in the above discussion of convergent and divergent thinking as elements affecting human thought. Such a frame has much use in times where many competing perspectives affect people's behavior.

Saturday, January 7, 2012

Since I figure a fair portion of you guys are interested in science, today I'm going to write something about cosmology.

One of the issues that faces cosmology and, to a lesser degree, astronomy, that the "hard sciences" like chemistry and some parts of physics don't have to deal with is the difficulty of performing experiments. Unless we physically send a space probe or rover, capable of performing experiments and sending back data to us, to whatever reach of space we're curious about, we only have observation to go on.

This is why we operated for over a millennium on the idea that Sol and the planets orbited Earth. When we saw retrograde motion ( http://www.lasalle.edu/~smithsc/Astronomy/retrograd.html - little need to read much of the article, just look at the animations if you're not familiar with it and you'll get it quickly), we decided that the planets moved around the Earth in cycles within cycles (as shown in the second animation on the foregoing link), called 'epicycles'. However, more precise observation showed that this could not account fully for the motion of the planets through the constellations, so enterprising astronomers added cycles within epicycles. The predictions the second-order epicycle model were also found wanting for predicting observation, so third-order epicycles were added, and so on. This could have gone on forever, nesting ever more cycles within cycles, and with computer programs of the type that create fractals, we might have modeled the position of the planets in the sky to an arbitrary degree of precision. (We would have had more difficulty modeling their distance, but we didn't know how to measure that back when we used the Earth-centric model.)

However, before we got computers, Copernicus came along and dredged up the old Greek model of planetary motion, where the planets, Earth included, all orbited Sol. Other astronomers gathered data on the planets' angular positions which would support a modified form of Copernicus' hypothesis, but it was only with Galileo that a powerfully convincing case was made that the planets all orbit Sol. If the data matched one model basically as well as the other, why bother changing the tried and (basically) true methods of calculating the planets' positions? But Galileo had the telescope, and with it he was able to overturn the main reason for believing in an Earth-centered cosmos: with his new tool of observation, he showed that Jupiter had moons orbiting it. If some things had been shown not to orbit the Earth, there was no longer reason to assume that everything orbited the Earth. Consequently, the Sol-centered model won out and now, 500 years later, some educated people still tacitly consider the Earth as the center of the universe, but when they think about it actively just about every educated person believes consciously if not unconsciously that we're on an approximate sphere that hurtles around Sol once every year.

(As an aside, it's interesting to note that under Galilean relativity of motion, we could make predictions just as correctly if we thought of Sol and Luna as orbiting the Earth, and the other planets orbiting Sol. With motion, any center location is as accurate as any other, but some are more convenient for thinking about certain types of things.)

Now, the reason I bring up this brief history lesson is to look at what it took to change paradigms. After Copernicus, some astronomers used the Earth-centered model for describing the positions of the planets, and others used the Sol-centered model. Neither of them disagreed very much in the observed data that their models predicted, but the method used by the two models to arrive at those predictions differed starkly. Now that we've had the telescope for four centuries, and sent out space probes into the solar system, we can say pretty definitively that the model where all the planets orbited the Earth in epicycles was flat-out wrong, and the only reason it made predictions that agreed with observation roughly as well as the Sol-centered model did was that it had centuries to accommodate itself to observation by adding more and more layers of epicycles. There wasn't really a competing theory to stomp it out, so it had plenty of time to adapt to its environment (Sol-centered theory at the time still used circular orbits, so the angular predictions of the Earth-centered model were actually more accurate the first time Sol-centered theory died out). Of course, once the environment it had adapted to changed with the ability to observe the sky in a new way, it lost out to its recently rejuvenated competitor.

Another thing that's worth looking at about this is the difference between the mindset that comes from believing everything in the cosmos orbits the Earth and that one that goes along with believing you're on an orb orbiting something else. With the perspective that cosmos revolves around your world, it's very much easier to believe in a deity who specifically had humankind in mind when creating the cosmos, but more importantly it's easy to take human assumptions and perceptions about the world as the world itself. With a Sol-centered perspective, the foibles of humanity seem not so much less significant as less universal. With the resurgence of the Sol-centered perspective came the widespread use of the scientific method, in which one tries to divorce one's ideas about the world from the human perspective to apprehend objective truth. With it has also come, after more time and further scientific discovery, the assumption among characters like Stephen Hawking that all human experience is an illusion created by the brain for the purposes of evolutionary survival. Others argue that treating mind as an exclusive property of humans is another form of Earth-centered thinking trying to sneak back in. At any rate, the transition to the Sol-centered perspective helped us tremendously insofar as developing technology at a remarkable speed, making a much larger portion of the population educated, and providing food for a greater portion of the human population is helpful.

Outside of astronomy, ideas about the cosmos provide a context for human lives. Thus, when we have multiple models that describe the same data, we have another criteria that lets us choose which to use for the moment: not only can we decide in terms of which one currently holds the minds of the scientific consensus or which one makes makes fewer major assumptions (deciding via Occam's razor), we can also decide in terms of which one provides a context for human lives that is more helpful for our survival as a species. These are all in absence of a new groundbreaking observation that lets us rule out some theories. To put it in Ramsey Dukes' terms, when it comes to selecting ideas about the cosmos, there's the purely Scientific method where a particularly groundbreaking observation rules out some models, but within the remaining models we have the Religious method where we operate under the authority of scientific convention, the Artistic method where we pick the remaining model that has the most parsimonious structure, and the Magical method where we chose from the models Science has not ruled out in terms of which would make the useful beliefs easy to access. (Remember that these decisions are only about models that observation has not ruled out - no matter how helpful or aesthetic it might be, people's experience with knots and other three dimensional objects would make it difficult to convince anyone that reality was actually two-dimensional.)

The reason that Science and the experimental method is more limited in the case of cosmology and must rely on Religion, Art, and Magic (note the capitalization - those terms mean a specific thing here as defined in the last paragraph) between discoveries of new tools of observation is that we can't actually do experiments with most of the things we hypothesize about in cosmology. Whereas with particle physics, we can observe, hypothesize, experiment, analyze our data, and form conclusions, with cosmology we are can only observe, hypothesize, analyze the data in terms of our hypotheses, and form tentative conclusions. The only way we can use experimentation to further cosmology is to extrapolate testable predictions from cosmological models, or develop tools of observation that might undermine the assumptions of certain models. So we can only use Science in some cases.

With the Religious method of selecting models, we put stock in whatever model most scientists, or the most authoritative scientists, have put their bets on. This is useful for forming a common framework for studying something, but it carries the problem of group-think and artificially maintained consensus with it. Consider the story of the ethologists who put ten chimps in a room with a banana hanging from a rope with a ladder under it. One of the chimps climbed the ladder to reach the banana and the experimenters electrified the floor, so the other chimps beat the crap out of him. They took a chimp out at random and replaced him with another, and of course he immediately made his way up the ladder. Again the scientists electrified the floor, and the other chimps attacked him. After a couple more times of this procedure, the scientists didn't need to electrify the floor to get the old apes to attack the new one who tried to climb the ladder for the banana. They scientists continued replacing apes after they stopped electrifying the floor, and even after all of the apes who had been electrified when their new fellow had tried to steal fire from the gods were gone, they still attacked new chimps who tried to climb the ladder. All of the old apes had been attacked when they tried to climb the ladder, so they attacked newcomers who tried to do the same. Deciding models purely based on consensus carries with it the issue that old, incorrect models might have incorporated ad hoc hypotheses (like cycles-within-cycles) over time to make themselves impervious to refutation by existing observation. If it's simply convention to lynch new chimps who try to climb the ladder, it means little to say that the floor doesn't get electrified anymore. More importantly than all that, though, at some point you can trace any consensus model back to when it was new.
So models can be maintained by the Religious method of model choice, but no model becomes the consensus by the Religious method.

Since all Scientific observations can be explained by multiple models (particularly with cosmology), and Religious consensus cannot explain why any model among many compatible with observation became consensus in the first place, we must trace all models back to their Artistic and Magical import. Occam's razor, the idea that we should not multiply explanatory entities more than necessary, is one of the basic Artistic principles for model selection. After it was realized by Maxwell that light propagates at a basically fixed speed as a changing magnetic field causing a changing electric field causing a changing magnetic field and so on, we could have added some ad hoc hypotheses to the idea of the Luminiferous Ether (the fluid through which electric and magnetic fields propagate as waves in 19th century models of electricity and magnetism) but it was far simpler to say that the fields simply propagate through space. So the Artistic method is a good way of getting rid of old hypotheses that are clinging on by a tenuous mesh of complication. Sometimes, however, it's difficult to assess whether one theory is more complex than another, particularly by scientists who are trained as experimenters rather than as logicians, so the Artistic method is most useful for telling us when observation has significantly ruled out a model, even though it has ad hoc hypotheses to justify why it was actually right all along, but just in a different form.

There have been few paradigm shifts made on Magical basis, but every paradigm shift has had Magical consequences. Germ theory, for instance, brought us a set of oblations which we perform before eating and, more importantly, before surgery, with which we consecrate our food and make gestures to ward off malign spirits when we sneeze. Similarly, Behaviorism - the idea, developed through experiments where organisms were treated as black boxes with only input and output, that systems of punishment and reward can teach any behavior to an organism that is biologically capable of it - had a profound impact on the public schooling system and child rearing. Many people use a Magical basis to decide which interpretation of Quantum Mechanics to use. Since there are many interpretations of QM which agree with the data, this is completely justifiable. (Of course some people take these interpretations and forget that they are derived from properties that operate at the minuscule scale of the quantum world, writing books like the Secret which are pure wish fulfillment and have lost all scientific basis, but have great sales figures. If consciousness can influence quantum indeterminacy, it would have to influence chaotic systems for its small-scale changes to have any noteworthy effects.)

Models of the fabric of the universe like the interpretations of Quantum Mechanics have a profound influence on our ideas about what we are and what we're made of, but cosmological models are at least as important - they affect the way we put our lives in context, and our ideas about "what it all comes down to." This is seen pretty profoundly if you contemplate for a moment that we're talking assemblages of bio-goop on a speck orbiting a spark in a corner of the universe that seems rather ordinary - a pretty good way to make everything in your life seem insignificant for a moment if things seem to stressful, but extended contemplation can lead to profound existential crises far beyond the scope of this discussion. And that's only the individual contemplation of an idea - when a nation or culture takes up a cosmological model in exclusion of others, that model is sure to have profound if subtle influences seen in the effects of the behavior of the people in that group.

Currently, the consensus model of cosmology is Big Bang theory. (Illustration: http://imgur.com/TlmWD ) For astronomers, in its most basic form it simply means interpreting the fact that we don't see a star at every possible point in the night sky in terms of the fact that the speed of light is finite and the idea that the universe has not been around long enough for light to get from everywhere to everywhere, and interpreting the fact that light from distant galaxies has a longer wavelength than light from closer galaxies in terms of the idea that the universe is expanding and cooling. For cosmologists, popular science writers, and the general public, it means that the universe came into being a particular duration of time ago, and has been expanding ever since, and will eventually either start contracting together until it smashes back into nothingness (the Big Crunch is less popular among scientists than it used to be) or it will eventually expand so much that information, heat, and energy will become basically meaningless. Heat Death is the favored end foreseen by cosmologists, it's not really surprising that our predictions of the cosmos' future and our rapid consumption of resources with little regard to sustainability reflect one another.

Currently still somewhat close to the fringes but gaining momentum are various hyperspherical models of the universe. These models describe an ageless universe with no beginning or end, where gravity exactly balances entropy, and life planets of infinite variety exist every now and then stretching beginninglessly back and endlessly on through time as stars are born and die, galaxies form and collapse, and the cosmos carries on. A hypersphere is the simplest four-dimensional shape, and since Einstein's principle of invariance we've known that all our calculations about constant speeds come out correctly if we treat time as the fourth dimension, perpendicular to the other three similarly to the way the three spatial dimensions are perpendicular to each other. A hypersphere has no outside which can be reached by entities inside it, but it also contains no boundary - just as you can go as far as possible on a globe in a straight line and get back to where you started, traveling twice the diameter of a hypersphere will bring you back to your starting point, and just like all straight-line paths you might take around a globe meet at both the point where you reside and the point on exactly the opposite side of the sphere, every location in a hypersphere has an antipode exactly one diameter-length from it in every direction.

[The simplest way to imagine a hypersphere is to think of two spheres whose surfaces touch. Not only do they touch at one point, but every point of their surfaces correspond with each other. If you draw two concentric circles, imagining the inner circle as the first sphere, the center of that circle is the center of the first sphere. The outer edge of the outer circle is the center point (compress it in your mind) of the second sphere, which comprises the part of the outer circle that isn't covered by the first sphere. You can think of it as two spheres next to each other, rolling to touch wherever you would cross between them. Of course, wherever you are on a hypersphere seems like the center of one of the spheres.]

In a hypersphere cosmos, the reason that we don't see stars in every possible place in the night sky is not because the stars haven't been around long enough, but because the cosmos is curved and we can't see past its horizon. The lengthening of light from distant galaxies happens because their light lenses through the curvature of the hypersurface (as shown here: http://imgur.com/YCL0q ) in the hypersphere model. In some versions of the hypersphere model, the cosmic microwave background radiation, which had to be filtered to remove the influence of nearby bodies before we got the most common picture of it, is gravitational radiation emitted in real time rather than something that a newborn universe made only at a certain stage in the process of its cooling. The fact that light lengthens at an increasing rate with distance rather than the linear one you'd expect with a uniformly expanding universe (explained in terms of negative pressure and accelerating expansion - "dark energy" as it's called - in the expanding cosmos model) is explained in terms of the fact that the the greater the distance between two points, the greater the lensing effect between them (lensing is added cumulatively since each point on the hypersurface bends the light, giving the increasing rate of lengthening with distance).

With small modifications, a hypersphere theory can be created that models most of the observations that big bang theory can be modified to model. Since the core difference between them lies in the interpretation of redshift, and subsequent differences result from the fact that one model looks to explain things in terms of the universe having a beginning and the other looks to explain things in terms of processes that can be carried out indefinitely in an ageless universe, and since cosmologists can't do experiments (caveat: there's at least one hypersphere theory that predicts novel and minute variations in the gravitation of different isotopes based on their nuclear structure rather than their nuclear mass, but which has not as of yet been tested due to lack of resources), we're left with a dilemma at least until Science comes along to save us.

The Religious consensus, of course, favors big bang theory, and will pull out tons of data interpreted in terms of big bang theory as evidence that it is correct. Being that it's the consensus, it has the manpower to interpret more data in terms of big bang theory than competing theories have to interpret data in their own terms, so the presentation of evidence interpreted in terms of the consensus theory without creating contradictions falls a fair bit short of proof. This evidence is of course still worth consideration, but quantity should not be a conclusive decision point, at least until we reach a point where the two sets of models are on equal footing in terms of manpower and resources for the type of Scientific tests mentioned parenthetically in the previous paragraph.

Likewise, the Artistic case is not conclusive. Hypersphere theory has on its side the fact that an ageless universe where time is relative makes more sense than a universe with an absolute age where time is relative, as well as the fact that the creation of a transfinite amount of mass-energy to fill a transfinite and expanding amount of space-time with relative uniformity would require an exception to the conservation of energy. Dark energy seems to fall under Occam's razor in some portrayals, but in a flat universe it has the beauty of perfectly balancing the force of gravity (if the universe is flat after all). Hyperspheric self-containment is simpler than an unbounded infinite quantity of space, but a set antipode length is just as arbitrary as a set age for the universe unless it can be defined in terms of fundamental quantities. Continuous gravitational radiation on the electromagnetic spectrum is not a possibility that is considered in the scientific consensus with the focus of Standard Model on finding a quantized force carrier particle for gravity, but if it is found to be the case in coming years it might make a more parsimonious explanation for the cosmic microwave background radiation. Finally, if the universe is curved into a hypersphere by virtue of the gravity of its own mass-energy as some models suggest, this might lead to both the acceleration experienced in the Pioneer anomaly and the unexpectedly fast spinning of galaxies that, decades ago, led scientists to postulate that a tremendous amount of undetected dark matter permeated galaxies and caused the increased angular speeds. Without further research, the Artistic case for the hyperspheric model is not conclusive, and without funds allocated to research that would test some of these possibilities, it is unlikely to become conclusive.

The Magical case is somewhat more conclusive, though there are still arguments to be made on each side. Big bang theory has the fact that a universe which has a beginning is much easier for humans to understand on its side, and with it the hope that a fairly complete history of the universe may eventually be developed. People with theological reasons to believe in creationism, such as Georges LeMaitre who proposed the theory in the first place, also have a better ally in big bang theory than they do in the hypersphere model. Since a great portion of the world's population believes the universe was created at some point in the past, this is a good Magical (if not Scientific) reason for exploring the possibilities of big bang theory fully before leaving it behind if we leave it behind at all. A universe with finite age also gives humans a greater cosmic importance in a way, since we are living in one of the most interesting times in the life of the universe. (It does not necessarily confer us special status as one of a finite number of sapient species however, given that space is infinite with relatively uniform mass-energy distribution in modern big bang theory.) If time goes on endlessly and uniformly, everywhere in the universe will have life at some point, over and over again in different permutations, making our status less special in comparison.

The hypersphere model has some points on its side as well. For one thing, the image of an intergalactic civilization having conquered so much of the universe but amounting to naught in the heat death of the universe is lifted from our mind's eye. This gives us incentive to pursue space exploration for its long-lasting fruits rather than with the rush we'd be in under big bang theory. Rather than rushing out to take what we could and conquer space, belief in an eternal universe would guide us to cultivate the universe like a garden rather than farm it until its nutrients were exhausted. The same perspective change would apply to our use of Earth's resources - we'd have a reason to preserve life while continuing to cultivate technology for expansion into space, and less incentive to develop technology at a breakneck pace in a rush to find a way to spread ourselves or our seeds to the stars before we destroy ourselves with the weapons made from that technology, or in the scarcity that results from a manic race toward further technology. With the emancipatory apocalypses written into the dominant monotheist paradigms and the nihilistic "take it before it's gone" written into the dominant materialist paradigm that atheists and other secular types turn to, an outlook like this is desperately needed. Further, if big bang theory has on its side that things with beginnings are familiar to humans, there's something intuitively natural about circles, spheres, and n-spheres for us as well. Besides those created by our limitations (either limitations of our capability or limitations we place on ourselves), we never encounter boundaries in the world, but horizons are quite familiar to us.

While big bang theory, besides the familiarities it holds, offers a sense of urgency to no ultimate purpose (in the currently triumphant heat death version of the theory particularly, but the big crunch is little better), the hypersphere model holds sustainability and the opportunity for as much continuity as reproducing living beings could ever want. It entices us into space with the possibility of infinite play rather than sending us out to claim spoils, and it heals us of some of the desperation of being alive in one of the only times that life is possible while being so silly as a species. It also alleviates the sense that without humanity expanding to the universe and beyond, the universe will be a meaningless non sequitur. Rather than pushing with the cruel hand of scarcity of resources and time to enjoy them, it pulls us back, urging us to slow down and enjoy our development rather than rushing to destroy each other before it's all gone, guiding us to be more playful with our existences. After all, who wants an eternity of seriousness?

To be clear, I'm not suggesting that we abandon big bang theory to solely pursue hypersphere models at this juncture. I only suggest that, in the absence of observations that irrevocably remove one or the other models (or both, wouldn't that be a wild surprise!) from the realm of possibility, we make our personal decisions with the possibility in mind that the universe could continue ever onward, and that we share our interest in the hypersphere possibility, if we find such interest within ourselves. Remember, cosmology is not hard science in the same way that chemistry is hard science - we cannot do direct experiments, so a more zetetic multi-model approach is better suited to the subject than a monolithic one.